Question: Simplify the following expression: $\sqrt{20}-\sqrt{80}+\sqrt{125}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{20}-\sqrt{80}+\sqrt{125}$ $= \sqrt{4 \cdot 5}-\sqrt{16 \cdot 5}+\sqrt{25 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{5}-\sqrt{16} \cdot \sqrt{5}+\sqrt{25} \cdot \sqrt{5}$ $= 2\sqrt{5}-4\sqrt{5}+5\sqrt{5}$ Finally, simplify by combining the terms. $= ( 2 - 4 + 5 )\sqrt{5} = 3\sqrt{5}$